Troops clashed with Muslim rebels holding at least 20 American and Filipino hostages in the southern Philippines yesterday, and the guerrillas said two of the hostages had been killed.

A spokesman for the Abu Sayyaf rebels, who kidnapped the hostages from a Philippine beach resort on Sunday, told a local radio station by telephone that the rebels would execute hostages if the fighting continued. He did not say which hostages died.

A Filipino woman, who sounded close to tears and told a local radio station that she was one of the hostages, appealed for the armed forces to halt their assault. "We are all right but these encounters are going to cost us our lives. We have children with us. I beg of you to please consider, to just sit down on the negotiating table and try and find a way to get everybody out safely," she added.

She said the three American hostages were with her group. President Gloria Macapagal Arroyo, an admirer of Britain's "Iron Lady" Margaret Thatcher, has vowed to crushed the group and has offered a reward of 100 million peso ($2 million) for information leading to capture of the kidnappers.

National security adviser Roilo Golez said that the government was standing by its no-ransom policy and insisting on the unconditional release of the hostages. "You know these reports, there is no confirmation, we are evaluating that. They might be using the radio station for disinformation," he said in a radio interview.

The military and the rebels differed over where the fighting was taking place, with the kidnappers saying that it was on the island of Jolo and the an armed forces spokesman saying it was on Basilan, an island 120 km (70 miles) to the north.

The military said that there had been casualties on Basilan but that they were still trying to identify who these were. "There are reported casualties but we are verifying who were wounded... One of our officers has been wounded," armed forces spokesman Brigadier General Edilberto Adan told reporters.

"We will not yet believe that," Adan said, referring to the rebel claim that two hostages had died in the shootout. "We are trying to confirm the report." Adan said that fighting on Basilan was continuing. "It is a jungle terrain where visibility is poor... You won't see anything 15 metres ahead of you," he added.

The Abu Sayyaf has an avowed goal of establishing an independent Muslim homeland in the south of the mainly Roman Catholic country, but its main interest appears to be kidnapping. Last year, they used similar tactics to seize more than 40 foreigners and Filipinos from nearby Malaysian resorts. All but one Filipino were freed, after payment of ransoms reputedly totalling millions of dollars, or escaped.

Abu Sayyaf spokesman Abu Sabaya did not say which hostages had been killed on Friday or make clear whether they were among the initial three Americans and 17 Filipinos abducted on Sunday. The Americans included a missionary couple.

Sabaya said the group had kidnapped an additional 10 people, mostly fishermen, since then. Last year, the Abu Sayyaf also said two hostages died in a clash with soldiers. The claim turned out to be unfounded.

They also threatened then to execute their hostages but never carried out the threat. "The Philippine government does not seem to care about the hostages... why should we?" Sabaya said on Friday, adding that if the assault continued they would begin executing hostages. "They are no relations of ours," he added.

He said that the assault began on Friday as the rebels and the hostages landed on Jolo, 960 km (600 miles) south of Manila. Sounds of gunfire could be heard in the background as the radio stations broadcast his calls. Sabaya had previously said Sunday's hostages had been divided into two groups, one heading for Jolo and one for Basilan.

General Adan said the fighting took place on the east of Basilan. "The operation is ongoing, contact with the terrorists is ongoing," he said. "This group whom we have encountered is holding hostages... This is like a cat and mouse game."

The woman who said she was a hostage was addressed by the radio station as "Ms. Ganzon". "I'm one of the hostages here, we are appealing, I am appealing, on behalf of all the other hostages, to please, please refrain from these military actions," she said. A Teresa Ganzon is on an official list of hostages.

Asked about the rebels' claim that two hostages had been killed, Ganzon said: "We got separated, that's what we heard, that there were two who got hurt, that's why we are begging you to stop this so that the others won't get hurt."